| Abstract: |
| First, a brief review of the existence and uniqueness of the Boltzmann-Enskog process is presented.
To construct a Boltzmann process, the existence of a solution $f$ of the Boltzmann equation for hard spheres is assumed. A stochastic differential equation driven by a Poisson random measure that depends on $f$ is introduced. The marginal distributions (in time) of its solution solve a linearized Boltzmann equation in the weak form. Further, if the distributions admit a probability density, we establish, under suitable conditions, that the density at each time $t$ coincides with $f$. The stochastic process is hence called a Boltzmann process.This is a joint work with S. Albeverio and B. Ruediger. |
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